System and Methods for Mapping and Demapping Digitized Signals for Optical Transmission

2. The method of claim 1, wherein the sign of the first and second symbols remains unchanged after mapping to the other respective symbol of the first and second symbols.

3. The method of claim 1, further comprising the step of applying a scrambling code to each input occurrence of the first and second symbols.

4. The method of claim 3, wherein the scrambling code comprises a periodic pseudo-random bit stream of 0 and 1 values having substantially equal probabilities of occurrence.

5. The method of claim 4, wherein, for each occurrence of the first symbol, the first symbol is mapped to the second symbol when the scrambling code has a 1 value, and the first symbol remains unchanged when the scrambling code has a 0 value.

6. The method of claim 3, wherein the scrambling code comprises a periodic pseudo-random bit stream of −1, 0, and 1 values, wherein the −1 and 1 values each have a 25% probability of occurrence, and wherein the 0 value has a 50% probability of occurrence.

7. The method of claim 6, wherein, for each occurrence of the first symbol, the first symbol is mapped to the second symbol when the scrambling code has a −1 or 1 value, and the first symbol remains unchanged when the scrambling code has a 0 value.

8. The method of claim 7, wherein, for each mapping of the first symbol to the second symbol, the symbol amplitude value of the mapped first symbol will be equal to the symbol amplitude value of the second symbol, the sign of the mapped first symbol will remain unchanged when the scrambling code has a 1 value, and the sign of the mapped first symbol will be reversed when the scrambling code has a −1 value.

9. The method of claim 1, wherein the first symbol has a ±1 value in the second symbol has a ±3 value.

10. The method of claim 1, wherein the series of transmitted symbols represents a PAM4 signal.

11. The method of claim 1, wherein the digitized signal is a DOCSIS 3.1 signal.

13. The mapping unit of claim 12, wherein the transmission link includes a transmitter portion at a first end of the transmission link and a receiver portion at a second end the transmission link opposing the first end.

14. The mapping unit of claim 13, wherein the processor is disposed proximate the transmitter portion and configured to perform digital signal shaping to generate the mapped signal.

15. The mapping unit of claim 14, wherein the processor is further configured to transmit a mapping code to the receiver portion.

16. The mapping unit of claim 15, wherein the processor is further configured to transmit the mapping code over a communication channel separate from the transmission link.

17. The mapping unit of claim 13, wherein the processor is disposed proximate the receiver portion and configured to perform digital signal unshaping to demap the mapped signal.

18. The mapping unit of claim 17, wherein the processor is further configured to demap the mapped signal using a mapping code received from the transmitter portion.

19. The mapping unit of claim 18, wherein the processor is further configured to receive the mapping code over a communication channel separate from the transmission link.

20. The mapping unit of claim 12, wherein the transmission link is configured for at least one of coherent detection and direct detection.